Infinity.

[Tinker Grey]

This is just wrong and it's easy to demonstrate if you think about it. If at any point any amount of mass "turned infinite" the resultant gravity would destroy the earth. The fact that we're here means that Holy Roller's misunderstood the concept.

On an related note, I'm still not sure of the point of this thread.

[/INDENT]

Kind of makes you worry about using your fire place or your grill, doesn't it?

 

[ArnautDaniel]

You misquote me, but never mind.

My bad - "expansion of the universe continues forever".

OK. I see. From such a radical empiricist p.o.v. certainly no actual infinities can exist -- at best potential ones.

But that leads me to ask -- do you believe that electrons exist, or only the measurements made on them?

Only the measurements.

But to be fair, even if I didn't take such a radical empiricist view, I'd say quantum field theory itself really doesn't say things like electrons exist between measurements either.

I'd say things like electrons are bundles of measurements that exist at the time of measurement.

QFTs include a notion that the number of particles being talked about isn't really fixed, and there is no sense in asking if two consecutive measurements of an "electron" are really measurements of the "same" electron.

QFT would seem to say it is meaningless to think of an electron continuing from measurement to measurement even if not interpreted in a radically empiricist sort of way.

 

[Holy Roller]

Again, having problems with the bolded phrasing: I don't understand what you mean by "an infinite yield of that .1% uranium mass." A maximal yield, perhaps, in that you're converting that fraction into pure energy output (splitting the atom is ridiculously energetic after all, at least in terms of the scales involved, due to mass-energy equivalence).

But not infinite. 200 MeV/fission is hardly infinite. Surely if this were true and we obtained infinite pure energy output, Trinity would have effectively wiped out the entire universe.



The Lorentz transforms are used to illustrate the alteration of mass and spacetime from the p.o.v of (or observation of) a particle whose velocities are close to c. However, the only way you're going to get "infinity" mass/energy out from them would be for the neutrons/U235 nuclei to be travelling at exactly c. However, this by definition requires that infinity energy be supplied / infinite work be done on the reactant particles, which is physically impossible. This is why c is the upper speed limit, if you like, of matter with non-zero rest mass.

The Lorentz transforms don't really apply in nuclear fission as you need slow neutrons so the U235 can capture them, hence cadmium/D20 moderator in nuclear reactors. (Ok, to be fair, you don't have moderators in nuclear weaponry as statistically you'll have a few slow ones but it's thus a hugely inefficient process). The only thing that does apply is mass energy equivalence, and that at most (per fission reaction) takes the rest mass of the U235+n combo (which will always be finite) and then releases the .1% as energy via E=mc^2, which is only ever finite also, about 200 MeV/reaction.

Not trying to be a pain here, I just really don't see how "infinity" applies to this scenario as the only time it ever applies are for scenarios that are physically impossible.

On reflection, there would be very few times in physics where actual infinities are involved? As an example, one can have a half decent gravitational model describing the orbit of a small body around a large body. You can keep the larger body fixed (infinite mass) and your model works fairly well, but if you want to be ultra-precise you've got to accept that it's not infinity and instead restore the finite mass of the larger body and work a barycentre into your model. Terrible example, I know - I was just pondering this discussion earlier, and I really am finding it quite hard to think of an actual physical infinity. Sure, you can approximate to infinity a lot of the time, but that's not quite the same thing.

This is like the only post worth replying to around here, but I digress...

Anyway. The idea of mass becoming infinite is impossible to understand (as is the concept of infinity itself), but seemingly present nonetheless. It can't be denied that the masses in this fission reaction are becoming infinite before becoming energy (gamma radiation). The best explanation I can come up with would be the fact that c is a finite quantity, yet can never be surpassed. Knowing that, the mass that turns into energy may likewise have a condition that's imposed on it, yet still may be infinite somehow.

Modern Physicists are also unclear on the concept. One hypothesis is that the massive particle in the fission reaction actually generates its antiparticle; the two annihilate, and the gamma rays (energy) get emitted thus. This is one approach that can bypass the infinity implications in E=MC2, but I feel uncomfortable with it, because we have an antiparticle that's being made, which goes against conservation laws.
What's your take on this hypothesis? Sound? Unsound?

 

[Holy Roller]

Cabal: about your suggestion that an infinite mass-before-energy would cause an infinitely strong field of gravity and thus swallow everything up isn't necessary, just as the worry over the new LHC collider generating mini-black holes is unfounded. If mini-black holes were generated from the new collider, there would be some kind of physical condition imposed on them that would make them affect only the space immediately around them, thus remaining relatively nonreactant to mass that's relatively far away.
In other words, although the mini-black hole would have infinite mass (it is a black hole, after all), it's still so darn small that its infinite mass wouldn't swallow up anything more than a few wavelengths away from it.

 

[Nathan45]

Cabal: about your suggestion that an infinite mass-before-energy would cause an infinitely strong field of gravity and thus swallow everything up isn't necessary, just as the worry over the new LHC collider generating mini-black holes is unfounded. If mini-black holes were generated from the new collider, there would be some kind of physical condition imposed on them that would make them affect only the space immediately around them, thus remaining relatively nonreactant to mass that's relatively far away.
In other words, although the mini-black hole would have infinite mass (it is a black hole, after all), it's still so darn small that its infinite mass wouldn't swallow up anything more than a few wavelengths away from it.

lol

 

[[serious]]

Cabal: about your suggestion that an infinite mass-before-energy would cause an infinitely strong field of gravity and thus swallow everything up isn't necessary, just as the worry over the new LHC collider generating mini-black holes is unfounded. If mini-black holes were generated from the new collider, there would be some kind of physical condition imposed on them that would make them affect only the space immediately around them, thus remaining relatively nonreactant to mass that's relatively far away.
In other words, although the mini-black hole would have infinite mass (it is a black hole, after all), it's still so darn small that its infinite mass wouldn't swallow up anything more than a few wavelengths away from it.

What on earth gave you the idea that black holes have infinite mass? They most certainly do not. They are a finite mass concentrated into a singularity (or can at least be treated as a singularity) The idea of the LHC is to create black holes of small mass to test a variety of theories. It could, for example, provide the first observation of hawking radiation. (required if black holes have some nonzero temperature)

Where on earth are you getting these ideas?

 

[ArnautDaniel]

What's your take on this hypothesis? Sound? Unsound?

Why do you keep persisting in pretending you understand anything about the science under discussion when everyone here agrees you don't?

 

[EnemyPartyII]

Beginning ---------- ∞, Infinite

∞ ----------------- End, Infinite

∞ ----------------- ∞, Infinite

Thus, Goddidit!

 

[Radagast]

But to be fair, even if I didn't take such a radical empiricist view, I'd say quantum field theory itself really doesn't say things like electrons exist between measurements either.

I'd say things like electrons are bundles of measurements that exist at the time of measurement.

There are people who take an equally hard line in mathematics, arguing that only (finite) computations and constructions exist. In which case infinity doesn't exist in mathematics either.

 

[Radagast]

In other words, although the mini-black hole would have infinite mass (it is a black hole, after all), it's still so darn small that its infinite mass wouldn't swallow up anything more than a few wavelengths away from it.

I don't think you understand the inverse-square law of gravity very well.

 

[Psudopod]

In other words, although the mini-black hole would have infinite mass (it is a black hole, after all), it's still so darn small that its infinite mass wouldn't swallow up anything more than a few wavelengths away from it.

Infinite mass you said. Doesn't matter how small the thing is; gravity is related to the mass of the object, not it's volume. You've not understood the point.

Kind of makes you worry about using your fire place or your grill, doesn't it?

Don't make toast! It could destroy the universe!!!!!!!!

 

[Wiccan_Child]

In other words, although the mini-black hole would have infinite mass (it is a black hole, after all), it's still so darn small that its infinite mass wouldn't swallow up anything more than a few wavelengths away from it.

A black hole does not have infinite mass. Try again.

 

[Cabal]

This is like the only post worth replying to around here, but I digress...

Anyway. The idea of mass becoming infinite is impossible to understand (as is the concept of infinity itself), but seemingly present nonetheless. It can't be denied that the masses in this fission reaction are becoming infinite before becoming energy (gamma radiation). The best explanation I can come up with would be the fact that c is a finite quantity, yet can never be surpassed. Knowing that, the mass that turns into energy may likewise have a condition that's imposed on it, yet still may be infinite somehow.

Modern Physicists are also unclear on the concept. One hypothesis is that the massive particle in the fission reaction actually generates its antiparticle; the two annihilate, and the gamma rays (energy) get emitted thus. This is one approach that can bypass the infinity implications in E=MC2, but I feel uncomfortable with it, because we have an antiparticle that's being made, which goes against conservation laws.
What's your take on this hypothesis? Sound? Unsound?

About your last paragraph - do you have any sources on this? It almost sounds like supersymmetry meets nuclear fission. And yeah, the antiparticle out of nowhere is a little bizarre. The idea of a process that's required to create a surplus of usable energy that also involves making exact duplicates of reactants beforehand? Also, how would annihilation give the same energy output (should really give a lot more) and somehow leave barium and krypton nuclei behind? Annihilation doesn't really like matter leftovers! Perhaps reading the sources will clear things up a little...

As for the rest of this quote - I'm sorry, but I still can't accept it. You're talking about the masses becoming infinite before becoming energy - the problem with this is, the only way they're going to gain mass (via relativity) is for enough energy to be supplied to them in the first place. If you claim the reactants reach an infinite mass, then conservation laws alone require that an infinite amount of mass/energy be supplied to the reactants. Again, it requires sourcing an impossible amount of energy and upon fission the release of an incredibly fatal amount of energy for all existence.

You keep saying that the mass becoming infinite and in doing so transforms into energy. Maybe I should point out that the E and p Lorentz transforms don't actually apply to photons? I'm assuming you got them from the wikipedia article on the Lorentz factor, it's further down the page. Sorry if you knew this already, but from trying to determine your train of thought, it seems like you think that the gamma photons have to follow the E and p Lorentz transforms too, and the only way to do that is to have the initial reactant mass go to infinity to get an appropriate Lorentz factor - but that isn't necessary as the E and p transforms will never apply to photons. Is this in any way relevant to what you were thinking?

Cabal: about your suggestion that an infinite mass-before-energy would cause an infinitely strong field of gravity and thus swallow everything up isn't necessary, just as the worry over the new LHC collider generating mini-black holes is unfounded. If mini-black holes were generated from the new collider, there would be some kind of physical condition imposed on them that would make them affect only the space immediately around them, thus remaining relatively nonreactant to mass that's relatively far away.
In other words, although the mini-black hole would have infinite mass (it is a black hole, after all), it's still so darn small that its infinite mass wouldn't swallow up anything more than a few wavelengths away from it.

Actually, I wasn't really suggesting anything gravitational. I just thought "infinite yield explosion = BAD."

I'm glad you mentioned black holes. It's already been pointed out that they don't contain infinite mass, but from the POV of someone being pulled into one at their very centre they have a gravitational singularity where density appears to go to infinity (again, black holes really aren't my strong point, so I'm loth to say that this is a good example of an infinity, maybe it's just apparently present because our understanding of the laws of physics breaks down at that point in spacetime).

So maybe we'll end up talking about black holes now - but I have to say, HR, I think we're all curious to know what the overarching point of this thread is?

 

[[serious]]

About your last paragraph - do you have any sources on this? It almost sounds like supersymmetry meets nuclear fission. And yeah, the antiparticle out of nowhere is a little bizarre. The idea of a process that's required to create a surplus of usable energy that also involves making exact duplicates of reactants beforehand? Also, how would annihilation give the same energy output (should really give a lot more) and somehow leave barium and krypton nuclei behind? Annihilation doesn't really like matter leftovers! Perhaps reading the sources will clear things up a little...

As for the rest of this quote - I'm sorry, but I still can't accept it. You're talking about the masses becoming infinite before becoming energy - the problem with this is, the only way they're going to gain mass (via relativity) is for enough energy to be supplied to them in the first place. If you claim the reactants reach an infinite mass, then conservation laws alone require that an infinite amount of mass/energy be supplied to the reactants. Again, it requires sourcing an impossible amount of energy and upon fission the release of an incredibly fatal amount of energy for all existence.

You keep saying that the mass becoming infinite and in doing so transforms into energy. Maybe I should point out that the E and p Lorentz transforms don't actually apply to photons? I'm assuming you got them from the wikipedia article on the Lorentz factor, it's further down the page. Sorry if you knew this already, but from trying to determine your train of thought, it seems like you think that the gamma photons have to follow the E and p Lorentz transforms too, and the only way to do that is to have the initial reactant mass go to infinity to get an appropriate Lorentz factor - but that isn't necessary as the E and p transforms will never apply to photons. Is this in any way relevant to what you were thinking?



Actually, I wasn't really suggesting anything gravitational. I just thought "infinite yield explosion = BAD."

I'm glad you mentioned black holes. It's already been pointed out that they don't contain infinite mass, but from the POV of someone being pulled into one at their very centre they have a gravitational singularity where density appears to go to infinity (again, black holes really aren't my strong point, so I'm loth to say that this is a good example of an infinity, maybe it's just apparently present because our understanding of the laws of physics breaks down at that point in spacetime).

So maybe we'll end up talking about black holes now - but I have to say, HR, I think we're all curious to know what the overarching point of this thread is?

It's sort of a divide by zero error. density is mass over volume. Black holes are singularities without volume. But yes, we can say black holes have infinite density. We can also say the gravitational field becomes infinitely strong as one gets infinitely close to the singularity (more of a limit than an actual infinity) Of course, neither of these can be directly dealt with or observed as they occur in a black hole (fundamentally unobservable) so they are still just mathematical constructs.

 

[ArnautDaniel]

There are people who take an equally hard line in mathematics, arguing that only (finite) computations and constructions exist. In which case infinity doesn't exist in mathematics either.

Yeah, there are people who do that too. And they have some fairly reasonable arguments on their side.

I think of mathematics as the development of consistent systems or consistent structures, or whatever you want to call it.

There is no reason not to object to introducing infinities in a reasonable and consistent way.

I think though, that with physical theories that one shouldn't assume that structures in the theory correspond to structures in nature when a clear physical measurement isn't involved.

This isn't quite radical empiricism rather it is a very conservative position on what we can deduce about nature from a physical theory or model.

 

[Holy Roller]

I don't think you understand the inverse-square law of gravity very well.

Lulz...

The inverse square law applies to all forces and radiations, Radagast, not just gravity.

 

[Holy Roller]

It's sort of a divide by zero error. density is mass over volume. Black holes are singularities without volume. But yes, we can say black holes have infinite density. We can also say the gravitational field becomes infinitely strong as one gets infinitely close to the singularity (more of a limit than an actual infinity) Of course, neither of these can be directly dealt with or observed as they occur in a black hole (fundamentally unobservable) so they are still just mathematical constructs.

More lulz...
[Serious], since density d is m/v, and if v=0 and d=infinity, wouldn't that mean that m=infinity?
And is the infinite mass just a "mathematical construct" (y/n)?

 

[[serious]]

More lulz...
[Serious], since density d is m/v, and if v=0 and d=infinity, wouldn't that mean that m=infinity?
And is the infinite mass just a "mathematical construct" (y/n)?

No. Not according to high school algebra, not according to calculus, not according to either quantum or classical physics.

1. x/0 =/= infinity, hence why I called it a "divide by zero error"
2. THERE IS NO INFINITE MASS. EVER. ANYWHERE.
3. The infinite density, as it can never be interacted with or observed under the uncertainty principle, is a mathematical construct.

 

[[serious]]

The inverse square law applies to all forces and radiations, Radagast, not just gravity.
(please, dear L-rd, please...)

No. Neither the strong nor the weak interactions follow the inverse square law. That's fully half the fundamental forces that don't.

 

[ArnautDaniel]

The inverse square law applies to all forces and radiations, Radagast, not just gravity.
(please, dear L-rd, please...)

I'm just going to say that the inverse square law (Newtonian gravity) is simply an approximation to Einsteinian gravity under certain nice conditions at this point, and that in general gravity doesn't obey an inverse square law.

I'm also going to say that the weak and strong nuclear forces do not obey an inverse square law.

HR - did you ever get past high school or freshman physics?